# ---
# title: 558. Logical OR of Two Binary Grids Represented as Quad-Trees
# id: problem558
# author: Tian Jun
# date: 2020-10-31
# difficulty: Medium
# categories: 
# link: <https://leetcode.com/problems/logical-or-of-two-binary-grids-represented-as-quad-trees/description/>
# hidden: true
# ---
# 
# A Binary Matrix is a matrix in which all the elements are either **0** or
# **1**.
# 
# Given `quadTree1` and `quadTree2`. `quadTree1` represents a `n * n` binary
# matrix and `quadTree2` represents another `n * n` binary matrix.
# 
# Return _a Quad-Tree_ representing the `n * n` binary matrix which is the
# result of **logical bitwise OR** of the two binary matrixes represented by
# `quadTree1` and `quadTree2`.
# 
# Notice that you can assign the value of a node to **True** or **False** when
# `isLeaf` is **False** , and both are **accepted** in the answer.
# 
# A Quad-Tree is a tree data structure in which each internal node has exactly
# four children. Besides, each node has two attributes:
# 
#   * `val`: True if the node represents a grid of 1's or False if the node represents a grid of 0's. 
#   * `isLeaf`: True if the node is leaf node on the tree or False if the node has the four children.
# 
#     
#     
#     class Node {
#         public boolean val;
#         public boolean isLeaf;
#         public Node topLeft;
#         public Node topRight;
#         public Node bottomLeft;
#         public Node bottomRight;
#     }
# 
# We can construct a Quad-Tree from a two-dimensional area using the following
# steps:
# 
#   1. If the current grid has the same value (i.e all `1's` or all `0's`) set `isLeaf` True and set `val` to the value of the grid and set the four children to Null and stop.
#   2. If the current grid has different values, set `isLeaf` to False and set `val` to any value and divide the current grid into four sub-grids as shown in the photo.
#   3. Recurse for each of the children with the proper sub-grid.
# 
# ![](https://assets.leetcode.com/uploads/2020/02/11/new_top.png)
# 
# If you want to know more about the Quad-Tree, you can refer to the
# [wiki](https://en.wikipedia.org/wiki/Quadtree).
# 
# **Quad-Tree  format:**
# 
# The input/output represents the serialized format of a Quad-Tree using level
# order traversal, where `null` signifies a path terminator where no node exists
# below.
# 
# It is very similar to the serialization of the binary tree. The only
# difference is that the node is represented as a list `[isLeaf, val]`.
# 
# If the value of `isLeaf` or `val` is True we represent it as **1** in the list
# `[isLeaf, val]` and if the value of `isLeaf` or `val` is False we represent it
# as **0**.
# 
# 
# 
# **Example 1:**
# 
# ![](https://assets.leetcode.com/uploads/2020/02/11/qt1.png)
# ![](https://assets.leetcode.com/uploads/2020/02/11/qt2.png)
# 
#     
#     
#     Input: quadTree1 = [[0,1],[1,1],[1,1],[1,0],[1,0]]
#     , quadTree2 = [[0,1],[1,1],[0,1],[1,1],[1,0],null,null,null,null,[1,0],[1,0],[1,1],[1,1]]
#     Output: [[0,0],[1,1],[1,1],[1,1],[1,0]]
#     Explanation: quadTree1 and quadTree2 are shown above. You can see the binary matrix which is represented by each Quad-Tree.
#     If we apply logical bitwise OR on the two binary matrices we get the binary matrix below which is represented by the result Quad-Tree.
#     Notice that the binary matrices shown are only for illustration, you don't have to construct the binary matrix to get the result tree.
#     ![](https://assets.leetcode.com/uploads/2020/02/11/qtr.png)
#     
# 
# **Example 2:**
# 
#     
#     
#     Input: quadTree1 = [[1,0]]
#     , quadTree2 = [[1,0]]
#     Output: [[1,0]]
#     Explanation: Each tree represents a binary matrix of size 1*1. Each matrix contains only zero.
#     The resulting matrix is of size 1*1 with also zero.
#     
# 
# **Example 3:**
# 
#     
#     
#     Input: quadTree1 = [[0,0],[1,0],[1,0],[1,1],[1,1]]
#     , quadTree2 = [[0,0],[1,1],[1,1],[1,0],[1,1]]
#     Output: [[1,1]]
#     
# 
# **Example 4:**
# 
#     
#     
#     Input: quadTree1 = [[0,0],[1,1],[1,0],[1,1],[1,1]]
#     , quadTree2 = [[0,0],[1,1],[0,1],[1,1],[1,1],null,null,null,null,[1,1],[1,0],[1,0],[1,1]]
#     Output: [[0,0],[1,1],[0,1],[1,1],[1,1],null,null,null,null,[1,1],[1,0],[1,0],[1,1]]
#     
# 
# **Example 5:**
# 
#     
#     
#     Input: quadTree1 = [[0,1],[1,0],[0,1],[1,1],[1,0],null,null,null,null,[1,0],[1,0],[1,1],[1,1]]
#     , quadTree2 = [[0,1],[0,1],[1,0],[1,1],[1,0],[1,0],[1,0],[1,1],[1,1]]
#     Output: [[0,0],[0,1],[0,1],[1,1],[1,0],[1,0],[1,0],[1,1],[1,1],[1,0],[1,0],[1,1],[1,1]]
#     
# 
# 
# 
# **Constraints:**
# 
#   * `quadTree1` and `quadTree2` are both **valid** Quad-Trees each representing a `n * n` grid.
#   * `n == 2^x` where `0 <= x <= 9`.
# 
# 
## @lc code=start
using LeetCode

## add your code here:
## @lc code=end
